Conventionally, by use of a sensitive film which is formed on the propagation path of the SAW device and a SAW sensor which measures an acoustic velocity variation caused by reaction of the sensitive film with gas molecules, highly sensitive gas sensors have been developed (see, for example, non-patent literature 1). Although the sensitivity of the sensor can be enhanced by increasing the interaction length of the SAW with the sensitive film, there is a limitation on an available interaction length due to diffraction caused by propagation.
On the other hand, it is possible to propagate a diffraction-free SAW which is naturally collimated on a spherical surface, when the aperture of the sound source of the SAW is selected to be the geometric mean of the diameter of a sphere and the wavelength of SAW, where the effect of diffraction caused by the propagation is balanced with that of focusing caused by the spherical surface (see, for example, patent literatures 1 and 2 and non-patent literature 2). A ball SAW sensor is the sensor utilizing this phenomenon which brings multiple roundtrips of the SAW on an equator with respect to the Z-axis cylinder of a piezoelectric crystal sphere and thus the interaction length of the ball SAW sensor is significantly increased compared with that in a planar SAW sensor (see, for example, non-patent literature 2). Since a variation in the delay time of the SAW caused by a variation in the velocity of the sensitive film is amplified in proportion to the number of the roundtrips, it is possible to perform a highly precise measurement of the delay time, resulting in realizing a highly sensitive gas sensor (see, for example, patent literatures 3 and 4 and non-patent literatures 2, 3, 4 and 5).
However, in order to effectively utilize this principle, it is necessary to perform temperature compensation with high precision, which remove a variation in the delay time caused by a variation in the velocity owing to a variation in the temperature of a device. Although a substrate with a crystal orientation of small temperature coefficient of the velocity can be used in the planar SAW sensor, such a substrate cannot be used in the ball SAW sensor because a crystal orientation is continuously changed along the propagation path. Although the temperature compensation can be realized by obtaining a difference between the outputs of equivalent devices with and without a sensitive film, it is not easy to make the temperature of the propagation path in one device identical to that in the other installed at separate location.
Here, since the temperature coefficient of relative velocity change of the piezoelectric crystal can be represented by a constant value independent of a frequency, for example, ppm/° C., relative delay time change is also independent of the frequency. On the other hand, since the relative delay time change caused by a variation in the velocity owing to reaction of the sensitive film with the gas molecules is proportional to the frequency, precise temperature compensation is realized by a difference of the relative delay time changes at two different frequencies on identical propagation path, typically represented by a unit of ppm, which is named as two-frequency measurement (TFM). A sensor capable of generating two frequencies is developed by use of a ball SAW sensor that can transmit and receive odd-order harmonics using a double interdigital electrode (see, for example, patent literatures 5 and 6 and non-patent literature 6).
In order to realize the measurement of the delay time change with sufficient precision for TFM, for example, it is necessary to use an analog-to-digital converter (ADC) with a sampling rate twice higher than the third harmonic frequency so as to record a waveform in the case of oversampling and to thereafter perform processing with a high time resolution such as a wavelet analysis (see, for example, non-patent literature 8). On the other hand, it is possible to measure the phase of the received signal using an ADC with low sampling rate, when the frequency of a received signal is reduced by heterodyne detection. (see, for example, patent literature 7 and non-patent literature 7).